Question

prime factorization of 572

Answer 1

First notice that 572 is an even number, then:

$\frac{572}{2}=286$

286 is an even number too, then:

$\frac{286}{2}=143$

now, a number is divisible by 11 if the digits that are on the even position minus the digits that are on the odds positions equals 0 or a multiple of 11, in this case we have 4-(3+1)=4-4=0, then 143 is divisible by 11:

$\frac{143}{11}=13$

since 13 is a prime number, the prime factorization of 572 is:

$572=2\cdot2\cdot11\cdot13=2^2\cdot11\cdot13$